ARTICLE IN PRESS

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doi:10.1016/j.ps

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Planetary and Space Science 55 (2007) 1584–1595

www.elsevier.com/locate/pss

Predicting the long-term solar wind ion-sputtering source at Mercury

Menelaos Sarantosa,�, Rosemary M. Killena, Danheum Kimb

aDepartment of Astronomy, University of Maryland, College Park, MD 20742, USAbGMV Space Systems, Rockville, MD 20850, USA

Accepted 10 October 2006

Available online 27 February 2007

Abstract

Maps of the precipitating solar wind proton flux onto Mercury’s surface are constructed using a modified Toffoletto–Hill (TH93)

model of the Hermean magnetosphere. Solar wind and IMF conditions around Mercury’s orbit near aphelion and perihelion,

respectively, were estimated by reanalyzing the Helios 40-s data for times when the spacecraft as in Mercury’s orbital range

(0.31–0.47AU). Probability density estimates obtained in this way allow us to quantitatively predict the likely range of the ion-sputtering

source as a function of true anomaly angle of the planet. Results indicate that the sputtering source along open fieldlines increases

fourfold from aphelion to perihelion, and that significant precipitation along closed fieldlines is twice as likely at perihelion due to finite

Larmor radius effects. We conclude that ion sputtering is comparatively more important as a source for the Hermean exosphere at

perihelion.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Mercury; Solar wind–magnetosphere interaction; Ion precipitation; Helios data

1. Introduction

Sputtering caused by precipitating solar wind ions hasbeen suggested as a source mechanism for the Hermeanexosphere (Potter and Morgan, 1990; Killen et al., 2001).This ion-sputtering source, which is regulated by theinteraction of the magnetosphere with the solar wind,may vary rapidly during transient events such as CMEs ordue to quasi-Alfvenic, small-scale turbulence in the solarwind which increases at small heliocentric distances(Marsch, 1991; Zurbuchen et al., 2004). In contrast, thelong-term precipitating flux onto Mercury’s low altitudesand surface is expected to vary smoothly from theHermean aphelion (0.47AU) to perihelion (0.31AU)following the general increase of plasma density andmagnetic field in the ambient solar wind. This variationof the solar wind input at Mercury due to orbital effectshas not been properly reflected in simulations previouslyperformed. We derived probability density estimates of thelong-term particle and field environments of Mercury

e front matter r 2007 Elsevier Ltd. All rights reserved.

s.2006.10.011

ing author.

ess: sarantos@astro.umd.edu (M. Sarantos).

obtained by the Helios I and II spacecraft to predict themost likely configurations of southward IMF. With theselikely boundary conditions for the magnetosphere, weanalytically computed the injected ion flux that precipitatesonto Mercury’s surface along open field lines close toperihelion (0.31AU) and aphelion (0.47AU). The distribu-tion function (phase space density) of ions injectedalong open field lines was reconstructed using the fieldlinegeometry derived by a modified Toffoletto and Hill (1993)model of the Hermean magnetosphere.Four basic types of magnetosphere models have been

developed for Mercury and used to study the solar windinteraction with the magnetosphere: three analytic models(Luhmann et al., 1998; Sarantos et al., 2001, Delcourtet al., 2002, 2003), a semi-empirical model (Massetti et al.,2003; Mura et al., 2005), a quasi-neutral hybrid model(Kallio and Janhunen, 2003, 2004), and two MHD models(Kabin et al., 2000; Zurbuchen et al., 2004; Ip and Kopp,2002, 2004). In broad terms their predictions agree: becauseMercury’s internal magnetic field is small, and its atmo-sphere is tenuous, solar wind ions can hit Mercury’s surfacealong open field lines (magnetic lines that have one endconnected to the solar wind). Large parts of the surface are

ARTICLE IN PRESSM. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1585

thus exposed to the solar wind. The footprint of openmagnetic field lines (‘‘cusp’’) contracts or expands respond-ing mainly to changes in the IMF. However, predictions ofdifferent models regarding the extent of the cusps and theamount of the plasma reaching the surface differ. Thesedifferences arise partly because different models capturedifferent parts of the physical processes, and partly becausedifferent input conditions were chosen.

It is very important to constrain boundary conditionsoutside of the magnetosphere: the IMF and solar windconditions. For instance, although the IMF radial compo-nent (Bx) is believed to be dominant at Mercury, manymodels used do not incorporate the effects of the IMF Bx(e.g., Luhmann et al., 1998; Delcourt et al., 2002, 2003;Massetti et al., 2003; Mura et al., 2005). In such Bx-freemodels it is necessary to apply high values of southwardIMF Bz to the magnetosphere to produce a realisticallyopen configuration. For example, Massetti presented caseswith IMF Bz ranging between �10 and �30 nT, whileDelcourt used a Bz ¼ �30 nT for his sodium photoiontracings. All cases which have been modeled previouslytested either perihelion conditions ðN ¼ 60276 cm�3Þ orextreme, CME-like conditions (Nsw ¼ 100 cm�3; vsw ¼

6002800 km=s) for the solar wind, and exploratory condi-tions for the IMF. These conditions, although possible, arenot typical of the solar wind along the Hermean orbit, andno realistic aphelion cases were modeled. Additionally,previous papers have told us nothing about how oftenthese configurations occur. To complement these results, asystematic approach was taken that establishes the mostprobable ion-sputtering rate at Mercury’s extreme orbitalpoints.

2. Multivariate statistical analysis of Helios 40-s data in the

0.31–0.47AU range

Probability estimates for input conditions for newmodeling runs of the Hermean magnetosphere and itsresponse to the solar wind were obtained by analyzing theHelios I and II 40-s data within Mercury’s orbital range.These spacecrafts explored the interplanetary mediumduring the ascending phase of solar cycle 21 between1975–1981. While previous work indicative of Mercury’sspace environment (Russell et al., 1988; Burlaga, 2001)presented one-dimensional histograms of probability den-sity functions for solar wind density, velocity, and IMF Bx,By and Bz based on Helios data and investigated how theseparameters scale with heliocentric distance, our objectivewas to visualize how these properties change concurrentlyin the solar wind, i.e., evaluate multivariate probabilitydensity estimates. For example, density and velocity in theambient wind are anti-correlated and therefore we mustselect their most likely conditions simultaneously. How-ever, with concurrent measurements missing in either theplasma or magnetometer data, the high-dimensional dataare frequently incomplete: our sample size represents about66 000 points at aphelion and 215 000 points at perihelion,

respectively. Thus, we did not have enough data foradequate bin sizes in the five-dimensional space. Instead,we treated the density–velocity and IMF Bx–Bz planesindependently. Our approach is essentially one of con-structing bivariate histograms with the following bin sizes:density, 1 cm�3; velocity, 10 km/s; and IMF Bx, Bz, 1 nT.More accurate probability density estimates can becomputed using an average shifted histogram method oreven a kernel density estimator (e.g., Martinez andMartinez, 2002). However, for the purpose of choosingself-consistent input conditions this present method willsuffice. The resulting probability density estimates of thedensity–velocity plane appear in Figs. 1a (around Hermeanaphelion) and b (around Hermean perihelion), while thosefor the IMF Bx–Bz plane are shown in Figs. 1c and d,respectively. Also shown in Fig. 2 are one-dimensionalhistograms describing probability densities at aphelion andperihelion, respectively, for density, velocity, IMF jBxj andIMF jBj.As expected, the solar wind velocity was found to be

independent of orbital distance while the density variedroughly as 1=r2 (Burlaga, 2001). A striking feature is thatthe velocity distributions have modes around 342 km/s (seeFig. 2b) for a wide range of likely density conditions(20260 cm�3 at aphelion; 502120 cm�3 at perihelion).Figs. 1a and b show that for the high-velocity cases, thereexists a small range of possible densities, but low density isconsistent with a wide range of velocity (400–700 km/s). Inspite of the extreme variability of the Hermean environ-ment, the Helios data averaged over 40 s reveal that theIMF Bx is the dominant component and that its variationfrom aphelion to perihelion largely follows that of the totalfield magnitude (compare Figs. 2c and d). The IMF Bx wasfound to be directed towards the Sun (plus) as likely asaway from the Sun (minus). The distribution of IMF Bx isbimodal (exhibiting towards and away sectors) but theeffect of its sign on the Hermean magnetospheric config-uration is North–South symmetric (Sarantos et al., 2001).For this reason, we only present the IMF jBxj in Figs. 1and 2. Likewise, the IMF Bz was not preferentially directedsouthward or northward as can be seen in Fig. 1.Comparing Figs. 1c and d, the distribution function(probability density) in the IMF Bx–Bz plane is signifi-cantly wider at perihelion. Thus, strongly southward IMFconfigurations ðBzo� 10 nTÞ are more likely at perihelion.However, since the IMF Bx is seen to increase faster fromaphelion to perihelion than the IMF Bz, models that do notincorporate Bx may be more descriptive of aphelionconditions.Consistent with this analysis of both the one-dimen-

sional and higher-dimensional data, we chose conditionsfor comparative runs between aphelion and perihelion inthe following way: we sampled five velocities between 342and 602 km/s, and chose self-consistent densities for whichthe aphelion probability distribution function in thedensity-velocity space is locally maximized. Three caseswith velocity 342 km/s were chosen reflecting the wide

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0 30 60 90 120 150 180 210

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city (

km

/s)

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)

0.1

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0.8

0.9Perihelion: 0.31−−0.34 AU

0 10 20 30 40

−30

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IMF

Bz (

nT

)

Probability density (x10−4

)

5

10

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z (

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14Perihelion: 0.31−0.34 AUAphelion: 0.44−0.46 AU

0 20 40 60 80 100

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Velo

city (

km

/s)

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0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

IMF (nT) IMF (nT)

Fig. 1. Probability density of solar wind conditions at Mercury in the density- V (a,b) and IMF Bx–Bz (c,d) planes computed from Helios I and II 40-s

plasma and magnetometer data for times when the spacecrafts were within Mercury’s aphelion (a, c) (0.44–0.46AU) and perihelion (b, d) (0.31–0.34AU)

range, respectively. The bin sizes in these plots are the following: density, 1 cm�3; velocity, 10 km/s; and IMF Bx, Bz, 1 nT. Note that while the distribution

of IMF Bx is bimodal (exhibiting towards and away sectors), a change in the polarity of Bx only reverses the hemisphere that is magnetically connected to

the solar wind. For this reason we only present the IMF jBxj in Figs. 1 and 2. Analysis of the high-dimensional data, along with the one-dimensional

probability densities shown in Fig. 2, allows us to quantify the likely range of the ion-sputtering source at Mercury using self-consistent solar wind input

for our magnetospheric model.

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951586

range of densities consistent with low-velocity solar wind.At perihelion, velocity choices remained the same, whileaphelion densities were increased by a factor of (0.47/0.31)2, or 2.3. The maximum density modeled at eitheraphelion and perihelion is somewhat higher than therespective nominal conditions (32 cm�3 at aphelion;73 cm�3 at perihelion). We tested IMF Bz cases rangingfrom �5 to� 10 nT (southward), keeping By ¼ 5 nTthroughout these runs, and readjusting Bx from theaphelion mode of �16 nT to the perihelion most likelyvalue of �34 nT. These decisions reflect the increase in totalfield magnitude and density from aphelion to perihelion.Our choices were made so that we can separately study theeffects on the precipitating flux of increasing particle

pressure and of the IMF turning more southward.Table 1 summarizes the input conditions used in oursimulations.The reader should be reminded that inherent in these

data are effects of the solar cycle activity. During the solarcycle 21 (1975–1986), solar activity minimum occurred latein 1975 and through the first half of 1976, while solarmaximum was reached in 1979–1980. The solar wind andIMF parameters analyzed in this work were collected byHelios over the first half of solar cycle 21 (1975–1981). Incontrast, missing measurements during the declining phaseof solar cycle activity (1981–1986) would result in widerdistributions for the IMF Bx, By, Bz, and total magnitudejBj as indicated by an analysis of Pioneer Venus Orbiter

ARTICLE IN PRESS

30 90 150 210

1

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Density (cm )

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Pro

b. d

ensi

ty (

x10

)

PerihelionAphelion

PerihelionAphelion

PerihelionAphelion

PerihelionAphelion

Fig. 2. (Clockwise from top left panel) Probability density plots of solar

wind density, IMF jBxj, IMF jBj, and solar wind velocity derived from

Helios 40-s data around Mercury’s aphelion (0.44–0.46AU) and

perihelion (0.31–0.34AU). The velocity is seen to be largely uncorrelated

to orbital distance, while the density responds as 1=r2. The change in IMF

jBxj follows that of the increase of the total field magnitude from aphelion

to perihelion, which confirms the dominance of the Bx component of the

IMF. These observations, coupled with plots in Fig. 1 showing how

density and velocity, as well as IMF Bx and Bz, change concurrently in the

solar wind, help fine tune our input conditions (Table 1).

Table 1

Input conditions for cases 1–5

Case Aphelion Nsw ðcm�3Þ V sw (km/s) Perihelion

Nsw ðcm�3Þ

1 9 602 21

2 16 532 37

3 22 342 50

4 27 342 62

5 35 342 80

In each case, scenarios of IMF Bz ¼ �5 nT and Bz ¼ �10nT were tested.

We chose Bx ¼ �16 nT at aphelion and Bx ¼ �34nT at perihelion and

kept By ¼ 5 nT throughout these runs. A total of 20 cases were thus

modeled to predict the likely range of the ion-sputtering source that is

consistent with the Helios data.

1975 1976 1977 1978 1979 1980 1981

10

12

14

16

18

20

Year

Rel

ativ

e sa

mpl

ing

freq

uenc

y (%

)

Helios data used in multivariate statistics

Fig. 3. Temporal variation of the relative sampling rate of Helios 40-s

data around the Hermean aphelion and perihelion. It is seen that the solar

wind parameters used in the multivariate analysis were not collected at the

same rates throughout the area of interest during solar activity minimum

and maximum periods. Especially incomplete appears the coverage of the

solar min conditions around aphelion. Since high-speed streams prevail

around solar minimum, the high-velocity, low-density area of the

density–velocity plane is patchy at aphelion (Fig. 1a). In contrast, the

same area was well-covered at perihelion (Fig. 1b).

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1587

(PVO) and IMP-8 data (Luhmann et al., 1993) taken at 0.7and 1AU, respectively, over the entire solar cycle 21.Particularly wider are the distributions of By and Bz, asthey respond not only to the variable solar surface field (asBx does), but also to the solar wind velocity, whosedistributions also exhibit a strong solar cycle dependence:at solar activity minimum, high-speed streams are morelikely since they are associated with coronal holes.However, the most likely values for the magnetic fieldpredicted here will be only slightly shifted towards highervalues, as the high-field tail counts ðjBzj420 nTÞ in PVOdata comprise at most 3% of all measurements during thedeclining phase of the solar cycle (see Luhmann et al., 1993,Fig. 14). Another source of temporal variation is intro-

duced into our sample because the solar wind parametersused in the multivariate analysis were not collected at thesame rates throughout the area of interest during solaractivity minimum and maximum periods. As is evident inFig. 3, the data around perihelion were collected mostly atsolar minimum and during the ascending phase of thecycle, while at aphelion there is a marked lack of datacollected at solar minimum. This explains why the high-velocity, low-density area of the density–velocity planeis patchy at aphelion (Fig. 1a) but smooth at perihelion(Fig. 1b): this is the regime of the high-speed solar windthat is persistent around solar minimum. While some biasis possible due to the aforementioned issues and to othersnot discussed here (e.g., possible sampling of respectiveheliocentric distances at different heliolatitudes each yearby separate spacecraft), it should be stressed that ourpurpose is not to assess effects of the solar activity cycle,but to provide reasonable estimates of the likely range ofconditions encountered at Mercury’s aphelion and perihe-lion due to the inherent variability of the solar wind.

3. Modeling the effects of injected ions: the distribution

functions

We compute the solar wind ion flux precipitating ontoMercury’s surface by analytically calculating the distributionfunction of ions injected through the magnetopause alongopen field lines. Our formulation is similar to that ofMassetti et al. (2003) with three key upgrades: (1) our model(TH93) handles the critically important IMF Bx, while the

ARTICLE IN PRESS

θSH

BSH

nBSPH

tθSPH

t

n

BSH

BSPH θSH

θSPH

LLBL Tail

Fig. 4. Schematic illustration of the angles ySH and ySPH in the Northern

hemisphere for (a) lines in the low-latitude boundary layer (LLBL) and (b)

lines stretched tailwards. BSH and BSPH are the magnetic field vectors in

the magnetosheath and magnetosphere, respectively; t is the tangent and n

the normal unit vectors at the magnetopause.

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951588

model used in the previous work (T96) does not; (2) we varyinput conditions from aphelion to perihelion self-consistentlyaccording to our analysis of the Helios 40-s data in the0.31–0.47AU range; and (3) we vary the Alfven velocity inthe solar wind self-consistently with our input, while Massettiet al. used a constant Alfven speed of 120km/s.

In the open magnetosphere, magnetosheath plasma gainsaccess into the magnetosphere mainly through the cuspregion. Usually visualized in the plane which contains themagnetic field and bulk velocity, injected magnetosheath ionshave a characteristic D-shaped distribution function (phasespace density) predicted theoretically as a result of magnetictension of fieldlines that have reconnected with the IMF(Cowley, 1982; Cowley and Owen, 1989; Lockwood andSmith, 1994; Lockwood, 1995) and observed both in theEarth’s dayside low-latitude boundary layer (LLBL) (e.g.,Fuselier et al., 1991) and, more recently, in the mid- andhigh-latitude cusp by Interball-Tail (Fedorov et al., 2000),POLAR (Fuselier et al., 2000), and Cluster (e.g., Bosquedet al., 2001; Lavraud et al., 2004). Key features of terrestrialcusp signatures, such as the cusp ion energy-latitudedispersion and the mid-altitude energy-pitch angle Vsignatures, have been successfully simulated (Onsager et al.,1993, 1995; Xue et al., 1997) by assuming that ions near themagnetopause are described by a truncated drifting bi-Maxwellian (Hill and Reiff, 1977). Farther into themagnetosphere, injected ion distribution functions evolveaway from a D-shaped to pancake or torus distributions asparallel velocity is converted to perpendicular velocity due togradient and curvature drifts or as a result of convection(e.g., Fedorov et al., 2000), and are usually accompanied bypopulations of magnetospheric origin.

We may reconstruct the part of the ion distribution thatcrosses the magnetopause (treated as a rotational disconti-nuity) and eventually impacts the Hermean surface asfollows. The tangential stress balance on either side of therotational discontinuity requires that the plasma bulk flow,

~V0

P;HT, in the de Hoffman–Teller frame (a frame that moves

with the discontinuity at the fieldline velocity, VHT) is field-

aligned at the Alfven velocity, ~VA (Cowley, 1982; Cowleyand Owen, 1989). Thus, the peak velocity (bulk plasma

speed) in Mercury’s frame, ~VP;M, is ~VP;M ¼ ~VP;HT þ

~VHT ¼ ~VA þ ~VHT (1) (Walen relation). Only magne-tosheath ions having positive parallel (field-aligned)velocities in the HT frame may enter the magnetospherein the northern hemisphere. In Mercury’s frame, thiscorresponds to injected ions having a cutoff velocity Vmin

which is the projection of the fieldline velocity VHT alongthe magnetospheric field direction:

Vmin ¼ VHT cos ySPH, (1)

while the peak and maximum velocities of the distributionare given by

VP;k ¼ VHT cos ySPH þ VA�SPH, ð2aÞ

VP;? ¼ VHT sin ySPH, ð2bÞ

Vmax ¼ VHT cos ySPH þ VA�SPH þ VTH, (3)

where ySH and ySPH are the angles of the magnetic field onthe magnetosheath and magnetosphere sides with the localtangent to the magnetopause (Fig. 4); , VTH is the thermalvelocity; and VA�SH, VA�SPH the Alfven velocity in themagnetosheath and magnetosphere, respectively. Last, thefieldline (open flux tube) moves away from the reconnec-tion site at the merging outflow velocity VHT:

VHT ¼ VSH � VA�SH cos ySH. (4)

Thus, assuming Earth-like precipitation at Mercury, theinjected ion distribution function (phase space density) oneach open field line in a planet-centered frame can beapproximated as

f ðV Þ ¼ nm

2pKT jj

� �1=2m

2pKT?

� �exp �

mðV jj � VP;jjÞ2

2KT jj

�

�mðV? � VP;?Þ

2

2KT?

�;VminpV jjpVmax,

f ðV Þ ¼ 0; V jjoVmin, ð5Þ

where n and m are the number density at the magnetopause(sheath side) and mass of solar wind protons, respectively;KT jj and KT? are the solar wind thermal energies parallel

and perpendicular to the local magnetic field; and V jj and

V? are the particle’s velocity in the magnetosphereimmediately after injection. The differential particle fluxis then computed as

J ¼2E2

m2

� �f ðVÞ. (6)

To compute (5) and (6) for each open fieldline, we need(a) the magnetosheath plasma population at the injectionpoint, (b) an estimate of the anisotropy between KT jj and

KT? for sheath ions, (c) an assumption about whatpercentage of sheath ions capable of transport actuallyget reflected back into the magnetosheath, and (d) anestimate of the loss cone angle at Mercury. The magne-tosheath plasma density, velocity and temperature in (3)are determined as polynomial fits derived from thegasdynamic code of Spreiter and Stahara (1980). To beconsistent with the Massetti et al. (2003) formulation, we

ARTICLE IN PRESS

4

2

0Z

–2

–4

2 0 –2

X

–4 –6

Fig. 5. Fieldline topology in the noon-midnight meridian plane produced

by the modified TH93 model of Mercury’s magnetosphere for a likely

aphelion configuration (density: 32 cm�3; velocity; 430 km/s; IMF

½�16 5�5� nT). Note that, due to the dominance of the IMF Bx, open

fieldlines turn towards the solar wind in the North, but away from it in the

South for this antisunward-directed radial IMF.

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1589

used a fit for Mercury provided in that paper as follows:

n

nSW¼ 3:3� 3:22d þ 1:4d1:5, ð7aÞ

T

TSW¼ 1þ 3ð1� ð�0:249d þ 0:953d1=2

Þ2Þ, ð7bÞ

V

VSW¼ �0:249d þ 0:953d1=2, ð7cÞ

where d ¼ dNOSE � dMP, the distance (measured along theGSM X- axis) from the subsolar point ðdNOSEÞ to the pointwhere the field line crossed the magnetopause ðdMPÞ. Self-consistent input for the asymptotic solar wind density andvelocity at Mercury is provided by our Helios analysis(Table 1). The solar wind temperature TSW is regulatedself-consistently from aphelion to perihelion by employinga relationship between the temperature and the speed forthe ambient solar wind developed by Lopez and Freeman(1986):

TSW½�103 K� ¼ ð0:0106VSW � 0:278Þ3=R½AU�,

VSWo500 km=s,

TSW½�103 K� ¼ ð0:77VSW � 265Þ=R½AU�,

VSWX500 km=s.

We assume that magnetosheath ions are anisotropic suchthat the perpendicular thermal velocity is twice the parallelthermal velocity, or T? ¼ 4T jj, which is justified by global

hybrid simulations of ion velocity distributions in themagnetosheath (Lin and Wang, 2002). In agreement withMassetti et al. (2003), we assume that half of themagnetosheath plasma on open fieldlines having therequired field-aligned velocity is pushed back intothe magnetosheath by the local Alfven wave. Lastly, wefollow the above authors in their estimate that the loss coneangle at Mercury is 351, and we map only those ions thatare injected with pitch angles up to 351off the localmagnetospheric field. However, we note that the loss coneangle could be computed self-consistently by the modelfrom the field magnitude at the magnetopause and thesurface field footpoint of each open line.

In the way described above, we can map the injectedphase space density and particle flux along open field linesat Mercury on the basis of the fieldline geometry (theangles ySPH and ySH) predicted by an open magnetospheremodel. To this end, we have modified the Toffoletto andHill (1989, 1993) magnetosphere model as described inresults previously published (Sarantos et al., 2001; Killenet al., 2001, 2004). Figs. 5 and 6 are an example of the fieldline configuration computed with our model for anaphelion configuration of the Hermean magnetosphere.In this application we computed the precipitating flux ontothe Northern hemisphere, which is the hemisphere thatconnects to the solar wind for the outward-directed Bxchosen here. We are currently expanding our scheme to thesouthern hemisphere, and will report those results alongwith simulations of the resulting Hermean exosphere in afuture publication. For a dominant IMF Bx the total

precipitating flux is expected to be roughly twice as high onthe hemisphere that is magnetically connected to the solarwind (Kallio and Janhunen, 2003).We must note that the method of analytically computing

distribution functions of injected ions described above doesnot accurately predict the latitudinal variation of the cuspsignatures. This is because, according to Liouville’stheorem, the phase space density is conserved, not alongfield lines, but along particle trajectories. Particles thatpenetrate the magnetopause at the same injection point butwith different pitch angles or energies impact the surface atdifferent locations due to the velocity filter effect. A moreaccurate approach, which was developed by Onsager et al.(1993, 1995), requires particle tracing. However, theadvantages of our method are that it correctly determinesthe integrated precipitating source along the entire openarea, without the need to know the electric field everywherein the magnetosphere, and that it has minimal computa-tional cost (Lockwood and Smith, 1994). Thus, it allows usto predict the long-term variation of the precipitatingsource from aphelion to perihelion.

4. Results

Detailed maps of the precipitating solar wind flux forlikely aphelion cases are presented in Figs. 7a–d (cases 1and 2). Comparative runs between aphelion and perihelion

ARTICLE IN PRESS

0 100 20045

50

55

60

65

70

75

80

85

90

Longitude

Latit

ude

thetaSHEATH

(degrees)

20

40

60

80

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120

140

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thetaSPHERE

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20

40

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Fig. 6. (a) Variation of the angle ySH in the Northern hemisphere between

the magnetosheath field and the local magnetopause tangent as Hermean

fieldlines evolve away from the reconnection site for the configuration

shown in Fig. 5. Large angles ð490�Þ indicate lines turned towards the

solar wind while small angles (�201) map to the tail; (b) variation of the

angle ySPH between the magnetopause tangent and magnetospheric field at

different injection points. Small angles ðo90�Þ indicate the location of the

low-latitude boundary layer (LLBL); the cusp proper lies at 901. Based on

the topology of open field lines we may compute the distribution function

and flux of precipitating ions along the entire part of Mercury’s surface

that is open to the solar wind.

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951590

are presented in Figs. 8a–d (cases 3 and 5). These mapsshow that the precipitating source is generally extended inlongitude (60–701). In all cases, the flux peaks within ashort latitudinal band at the LLBL ðySPHo90Þ but dropsoff rapidly by two orders of magnitude or more within15–201of latitude away from the open–closed boundary.This is easily understood from cusp signatures in theEarth’s magnetosphere: the resulting bulk flow in themagnetosphere is primarily away from the planet’s surfacealong fieldlines that map to the tail, but towards the surface

and more field-aligned for lines that cross in the dayside.However, a unique feature of the Hermean magnetospherearises because the dominant Bx component introduces adawn–dusk asymmetry in the shape of the cusps: the cuspis very asymmetric for the IMF Bz ¼ �5 nT cases, butbegins to straighten and become more symmetric as Bzbecomes comparable to Bx (e.g., compare Figs.7a, c withFigs. 7b, d). The first open fieldline is typically located at40–451Northern latitude, but the cusp may be pushedfurther equatorward to 25–301 for high-velocity, high Bzconditions that are likely at perihelion (cases 1 and 2).Maps showing the effective open area (fieldlines that

cross the magnetopause within 2RM down the tail) and ofthe integrated precipitating source for likely conditions ofthe solar wind and IMF, including Bz ranging from �5 to�10 nT, are presented in Figs. 9a, b. Up to 20% of theentire northern hemisphere could be open to the solar windfor strongly southward conditions at perihelion. Increasingdynamical pressure within the high-velocity regime resultsin substantial change in the precipitating area, whilepressure increases in the low-velocity regime affect thearea available to the solar wind rather weakly. On the otherhand, the precipitating flux seems to vary little withinaphelion conditions (Fig. 7) but clearly increases atperihelion (Fig. 8) both in the dayside and in the tail. Infact, Fig. 9b demonstrates that the integrated precipitatingsource ðs�1Þ increases by a factor of 4 for comparativesouthward IMF Bz ¼ �10 nT conditions from aphelion toperihelion. In contrast, photon-stimulated desorption(PSD), which is believed to be the main source mechanismfor the Hermean exosphere (McGrath et al., 1986; Madeyet al., 1998), is expected to increase as the solar UV flux by1=r2 (quiet Sun conditions), or by a factor of 2.3 fromaphelion to perihelion (Smyth and Marconi, 1995). Clearly,the modeled ion-sputtering source increases faster thanPSD. This result implies that a larger fraction of theHermean exosphere is due to sputtering caused by the solarwind at perihelion. Note that to determine the relativeimportance of these mechanisms, one must account for thesputter yield as well as the source rates (see Killen et al.,2001, 2004; Lammer et al., 2003, and references therein).Consequently, the determination of the relative importanceof each mechanism requires the coupling of the magneto-sphere model to a model of the Hermean exosphere (e.g.,Killen et al., 2001). We do not presently compare yields forthese two processes nor for impact vaporization, which isalso a possible source mechanism for the exosphere;instead, we only identify trends.A comparison with the Massetti et al. (2003) predictions

for a comparable case with VA ¼ 120 km=s, Pdyn ¼ 20 nPaand Bz ¼ �10 nT shows that inclusion of a strong Bx ¼�16 nT increases fluxes by a factor of 3. This is expectedbecause the IMF Bx leads to increased precipitation at theLLBL: fieldlines turn forward, cross the magnetopausecloser to the subsolar nose, and the bulk flow is more field-aligned. The same physical reasons explain the increaseof the precipitating flux from aphelion to perihelion.

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0 50 100 150 200

30

40

50

60

70

80

90

Longitude

La

titu

de

Log10

Flux (cm s )

7.5

8

8.5

9

9.5

0 50 100 150 20030

40

50

60

70

80

90

Longitude

La

titu

de

Log10

Flux (cm s )

7.5

8

8.5

9

9.5

0 50 100 150 20030

40

50

60

70

80

90

Longitude

La

titu

de

Log10

Flux (cm s )

7

7.5

8

8.5

9

9.5

0 50 100 150 200

30

40

50

60

70

80

90

Longitude

La

titu

de

Log10

Flux (cm s )

7.6

7.8

8

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

a b

c d

Fig. 7. Precipitating flux (log scale) of solar wind ions impacting Mercury’s surface for aphelion cases 1 (a, b) and 2(c, d) outlined in Table 1. Two sets of

plots are produced with Bz ¼ �5nT (a, c) and Bz ¼ �10nT (b, d) while Bx ¼ �16nT and By ¼ 5nT. Vertical columns (a vs c; b vs d) address the effects

of increasing pressure on the cusp location and precipitation flux for the same IMF, while horizontal rows (a vs b; c vs d) illustrate the effects of a more

southward IMF for given pressure. The open-closed boundary exhibits a strong dawn-dusk asymmetry for the Bz ¼ �5nT as a result of the dominant Bx.

In turn, the cusp becomes more symmetric as Bz grows comparable to Bx (cases with Bz ¼ �10 nT).

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1591

Compared to aphelion conditions, the solar wind flux is higherdue to the higher density, the magnetopause is closer to thesurface, and the maximum energy, Emax, of the injected ionsalong each open line is higher both in the LLBL and,especially, in the cusp proper for perihelion configurations.

The picture of precipitation presented by the analyticalmodel is incomplete because it tells us nothing aboutprecipitation occurring along closed field lines. Since theHermean magnetosphere is small, the Larmor radius ofsolar wind protons is often expected to be comparable tothe magnetopause and bow shock distances thus resultingin significant precipitation along closed fieldlines. Thiseffect is evident in simulations of solar wind impactperformed with a hybrid model (Kallio and Janhunen,2003) showing that solar wind ions penetrate a larger area

than that directly connected to open field lines. Using theHelios 40-s data for Mercury, we modeled the distributionof the predicted TH93 magnetopause nose distance underthis input (Fig. 10a) and computed the distribution ofobserved proton gyroradius in the solar wind. This allowedus to quantify the probability of substantial precipitationoccurring due to the finite Larmor radius effect. Using anarbitrary threshold of rL=dnose ¼ 0:4 for significant pre-cipitation on closed fieldlines, we find that the tail of thedistribution is wider at perihelion by about a factor of 2 inprobability space (Fig. 10b). These results point out thatthe precipitating source may frequently increase by morethan a factor of 4 from aphelion to perihelion when oneaccounts for the higher likelihood of high Larmor radii ofsolar wind ions for conditions typical at perihelion.

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0 50 100 150 20030

40

50

60

70

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90

Longitude

Latit

ude

Log10

Flux (cm s )

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

9.8

10

0 50 100 150 20030

40

50

60

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Latit

ude

Log10

Flux (cm s )

7.5

8

8.5

9

9.5

0 50 100 150 20030

40

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Longitude

Latit

ude

Log10

Flux (cm s )

8.5

9

9.5

10

0 50 100 150 20030

40

50

60

70

80

90

Longitude

Latit

ude

Log10

Flux (cm s )

7.8

8

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

a b

c d

Fig. 8. Precipitating flux (log scale) of solar wind ions impacting Mercury’s surface for likely aphelion and perihelion conditions (cases 3 and 5 of Table 1).

These maps are produced with IMF Bz ¼ �10 nT and By ¼ 5 nT while at aphelion Bx ¼ �16nT (a, c) and at perihelion Bx ¼ �34 nT (b, d). Responding

to the denser plasma and stronger field magnitude, the precipitating flux at perihelion clearly increases both in the dayside and in the tail.

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951592

5. Conclusions

To quantify the systematic variability of the ion-sputtering source between the Hermean aphelion andperihelion, we reconstructed the distribution functionsand precipitating flux of solar wind protons in the openfield line region using a modified TH93 model of Mercury’smagnetosphere. To determine realistic input conditions weanalyzed the Helios I and II 40-s data at times when thespacecraft were within Mercury’s orbital range, and com-puted multivariate probability density estimates (Fig. 1).Consistent with these estimates, which are presented herefor the first time for Mercury, we modeled a wide variety ofconditions in velocity (342–602 km/s) and density space(aphelion: 9235 cm�3; perihelion: 21280 cm�3) chosen

self-consistently (Table 1). For the IMF, we tested south-ward conditions ðBz ¼ �5;�10 nTÞ coupled with the mostlikely self-consistent IMF Bx measured by Helios (aphe-lion: �16 nT; perihelion: �34 nT). We report that theinclusion of the dominant IMF Bx component raised themodeled precipitating flux by a factor of 3 over cases ofcomparable density, velocity and IMF Bz but without Bx.In addition, the likely range of the precipitating source isamplified by a factor of 4 from aphelion to perihelionconditions, while the area open to the solar wind increasesby a factor of 2. Therefore, we anticipate that ionsputtering is a more important source for the Hermeanexosphere at perihelion.Maps of the precipitation predicted by the analytical

model are simplified in three ways. First, they do not

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1 2 3 4 56

8

10

12

14

16

18

20

22

Case index

Effective O

pen A

rea

% of Northern Hemisphere

1 2 3 4 50

2

4

6

8

10

12

14

16x 10

25

Case index

Pre

cip

itating s

ourc

e (

s−1

)

Aphelion, Bz = −5nT

Aphelion, Bz = −10nT

Perihelion, Bz = −5nT

Perihelion, Bz = −10nT

Fig. 9. (a) Effective open area and (b) integrated precipitating source ðs�1Þ

from the Hermean aphelion to perihelion for different conditions of the

solar wind and IMF. It is seen that when the IMF Bx is dominant, the

effect of IMF Bz is small provided that it is southward. The precipitating

source increases by a factor of 4 at perihelion, while the area available to

solar wind impact doubles.

0.5 1 1.5 2 2.5

0

5

10

15

20

Nose Distance from Center [Rm]

Fre

qu

en

cy [

%]

Helios 1 & 2 Data

Date: 1975 − 1981

Range: 0.31 − 0.46 AU

Weibull Fit

Dipole moment [nT R3]

330

350

400

450

0.3 0.4 0.5 0.6 0.70

0.01

0.02

0.03

Pro

ba

bili

ty d

en

sity

High-end tail

0.1 0.2 0.3 0.4 0.50

0.05

0.1

Proton gyroradius/Magnetopause distance

Pro

ba

bili

ty d

en

sity

Main body of distribution

Aphelion

Perihelion

Aphelion: 2.4%

Perihelion: 5.6%

Fig. 10. (a) distribution of the modeled TH93 magnetopause nose

distance under the 40-s Helios input for different choices of magnetic

dipole moment consistent with the Mariner 10 data; (b) distribution

function of the solar wind Larmor radius to magnetopause distance for

dipole moment of 350 nT R3. The tail of the distribution (upper panel) is

wider at perihelion by about a factor of 2. Thus, precipitation along closed

fieldlines due to the finite Larmor radius is expected to be twice as likely at

perihelion.

M. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–1595 1593

describe contribution by precipitating solar wind ions onclosed field lines due to finite Larmor radius effects. Tosupplement our predictions, we investigated how the ratioof the observed proton gyroradius over the TH93-modeledmagnetopause distance changes from aphelion to perihe-lion according to the Helios data. Results indicate thatsignificant precipitation on closed field lines is twice aslikely at perihelion than at aphelion. Thus, the finiteLarmor radius effect will tend to further accentuate theincrease in precipitation from aphelion to perihelion.Second, the simple magnetopause pressure balance per-formed in the modified TH93 model does not include

induction effects caused by finite surface conductivity.Surface-induced currents, which may contribute 10% ofthe interior field, oppose the transfer of magnetic flux fromthe dayside to the tail ðBzo0Þ and may substantially affectthe magnetospheric topology and dynamics (Glassmeier,2000; Grosser et al., 2004; Janhunen and Kallio, 2004). Amore realistic magnetopause may resist extreme compres-sion by the solar wind. As the dayside magnetic fieldintensifies at low altitudes due to surface inductioncurrents, injected particle trajectories will be affected bythe added magnetic field, which may prevent penetration tothe planetary surface. It may be that only field-alignedparticles precipitate down to the low-altitude ionosphere

ARTICLE IN PRESSM. Sarantos et al. / Planetary and Space Science 55 (2007) 1584–15951594

and surface, much like the case in the Earth’s magneto-sphere. Lastly, the extent to which possible pickup of heavyexospheric ions (e.g., Naþ, Kþ, Oþ) may alter the solarwind flow and affect the bow shock and magnetosphericboundaries has not been considered here. Thus, ourcomputations should be considered as only a first-steptowards quantifying the response of the magnetospher-e–exosphere system to extreme solar wind environments atMercury’s aphelion and perihelion.

Acknowledgements

This work was supported by the NASA GeospaceSciences Program Grant NNG04G195G. Helios 40-s datawere kindly supplied by R. Schwenn. The original versionof the TH93 model was provided by F. Toffoletto (RiceUniversity). The authors would like to thank H. Rosen-bauer and F. Neubauer for making Helios data available tothe scientific community, and P. Reiff for numerousdiscussions and helpful comments on this paper.

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